FINDING THE VOLUME OF A CONE WORKSHEET

Question 1-4 : Find the volume of cone shown below. Round your answer to the nearest tenth if necessary. Use the approximate of value of π, that is 3.14.

Question 1 :

Question 2 :

Question 3 :

Question 4 :

Question 5 :

The volume of a solid right circular cone is 11088 cm³. If its height is 24 cm then find the radius of the cone.

Question 6 :

The ratio of the volumes of two cones is 2:3. Find the ratio of their radii if the height of second cone is double the height of the first.

Question 7 :

The volumes of two cones of same base radius are 3600 cm³ and 5040 cm³. Find the ratio of heights. 

Question 8 :

If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.

Question 9 :

A conical container is fully filled with petrol. The radius is 10m and the height is 15 m. If the container can release the petrol through its bottom at the rate of 25 cu. meter per minute, in how many minutes the container will be emptied. Round off your answer to the nearest minute.

Question 10 :

If the radius of the base of a cone is tripled and the height is doubled then the volume is 

a) made 6 times      b) made 18 times

c)  made 12 times     d) unchanged

1. Answer :

Step 1 :

Write the formula to find volume of a cone.

V = 1/3 · πr²h

Step 2 :

Substitute the given measures.

V ≈ 1/3 · 3.14 · 2² · 8

Simplify.

V ≈ 1/3 · 3.14 · 4 · 8

V ≈ 33.5

So, the volume of the given cone is about 33.5 cubic inches.

2. Answer :

Step 1 :

Write the formula to find volume of a cone.

V = 1/3 · πr²h -----(1)

Step 2 :

To find the volume, we need the radius of the cone. But, the diameter is given, that is 8 ft. So, find the radius.

r = diameter/2

r = 8/2

r = 4

Step 3 :

Substitute π ≈ 3.14, r = 4 and h = 9 in (1).

V ≈ 1/3 · 3.14 · 4² · 9

Simplify.

V ≈ 1/3 · 3.14 · 16 · 9

V ≈ 150.7

So, the volume of the given cone is about 150.7 cubic feet.

3. Answer :

Step 1 :

Write the formula to find volume of a cone.

V = 1/3 · πr²h -----(1)

Step 2 :

To find the volume, we need the radius of the cone. But, the diameter is given, that is 15 cm. So, find the radius.

r = diameter / 2

r = 15/2

r = 7.5

Step 3 :

Substitute π ≈ 3.14, r = 7.5 and h = 16 in (1).

V ≈ 1/3 · 3.14 · 7.5² · 16

Simplify.

V ≈ 1/3 · 3.14 · 56.25 · 16

V ≈ 942

So, the volume of the given cone is about 942 cubic cm.

4. Answer :

Step 1 :

Write the formula to find volume of a cone.

V = 1/3 · πr²h

Step 2 :

Substitute the given measures.

V ≈ 1/3 · 3.14 · 2² · 3

Simplify.

V ≈ 1/3 · 3.14 · 4 · 3

V ≈ 12.6

So, the volume of the given cone is about 12.6 cubic feet.

5. Answer :

Volume of a solid right circular cone = 11088 cm³

height = 24 cm

1/3 · πr²h = 11088

(1/3) · 3.14 r²(24) = 11088

8 · 3.14 r² = 11088

r² = 11088 / (8 x 3.14)

r² = 441.40

r = √441.40

r = 21

So, the radius of cone is 21 cm.

6. Answer :

Volume of first cone : Volume of second cone = 2 : 3

r₁ and r₂ be the radii of two cones

h₁ and h₂ be the height of cones

h₂ = 2 h₁

(1/3)π r₁²h₁ / (1/3)π r₂²(2h₁) = 2/3

r₁²h₁ / r₂²(2h₁) = 2/3

r₁²/ 2r₂² = 2/3

r₁²/ r₂² = 4/3

(r₁ / r₂)² = 4/3

(r₁ / r₂) = √(4/3)

(r₁ / r₂) = 2/√3

r₁ : r₂ = 2 : √3

So, the ratio between radii is 2 : √3.

7. Answer :

r₁ and r₂ be the radii of two cones

Here r₁ = r₂

h₁ and h₂ be the height of cones

(1/3) πr₁²h₁ / (1/3) πr₁²h₂ = 3600/5040

h₁ /_h2 = 360/504

h₁ /_h2 = 5 / 7

h₁ : _h2 = 5 : 7

So, the ratio of height is 5 : 7.

8. Answer :

Circumference of a conical wooden piece = 484 cm

2πr = 484

2 x 22/7 x r = 484

r = (484 x 7)/44

r = 77

height = 105

Colume of cone = (1/3) πr²h

= (1/3) x 3.14 x 77²x 105

= 651597.1 cm³

9. Answer :

radius = 10 m

height = 15 m

Speed = 25 cu. meter per minute

Volume of petrol in the container = (1/3) πr²h

= (1/3) x 3.14 x 10²x 15

= 1570 m³

Time taken to empit = volume / speed

= 1570/25

= 62.8 minute

Approximately 63 minutes.

10. Answer :

Radius and height of cone be r and h.

New radius = 3r

new height = 2h

Volume of new cone = (1/3) π(3r)²(2h)

= (1/3) π(9r²)(2h)

= 18 [(1/3) πr²h]

= 18 (volume of cone)

So, option b is correct.

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